Theorems · Theorem · commutative algebra
Algebra.trace_eq_of_algEquiv
∀ {A : Type u_7} {B : Type u_8} {C : Type u_9} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : CommRing C]
[inst_3 : Algebra A B] [inst_4 : Algebra A C] (e : B ≃ₐ[A] C) (x : B),
(Algebra.trace A C) (e x) = (Algebra.trace A B) x- Defined in
- Mathlib.RingTheory.Trace.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement and proof · cited by 10,215
- AlgEquivstatement and proof · cited by 1,681
- map_mulproof · cited by 1,137
- LinearMap.extproof · cited by 844
- AlgEquiv.symmproof · cited by 615
- DFunLikeproof · cited by 576
- AlgEquiv.toLinearEquivproof · cited by 117
- Algebra.tracestatement · cited by 90
Cited by4
Results whose statement or proof uses this declaration.
- Algebra.trace_eq_of_equiv_equivproof · cited by 3
- not_dvd_differentIdeal_of_isCoprime_of_isSeparableproof · cited by 2
- Algebra.discr_eq_discr_of_algEquivproof · cited by 1
- dvd_differentIdeal_of_not_isSeparableproof · cited by 1